# How to calibrate the time constraint of an exam for a new course?

I am preparing an exam for a course I'm running. It's an engineering course; the exam problems require students to apply conceptual knowledge and quantitative skills taught in lectures and labs.

It's the first time the class has been offered, so I don't have a frame of reference from previous years. There haven't been any in-class quizzes or other opportunities for me to find out directly how long students would take to solve problems similar to the ones on the exam. I also haven't found any similar exams from other universities to serve as a reference.

Obviously, I am much more experienced in the material than my students, so I can't really generalize from how long it takes me to solve these kinds of problems.

This question is for the more experienced educators out there: in a scenario like this, are there any methods or general rules for determining how long you can make the exam, given the time allotted?

I don't want time to be a major issue on this exam; I want most students who are reasonably well prepared to be able to complete the exam in the given time.

• Just an idea: let a TA (or some doctoral student who is familiar to the topic) solve the problems you have in mind. The TA should be as fast as one of the best students so you can add 20%-50% of the time needed to the exam length. The doctoral student is probably much slower(as he is not used to the kind of problems and sometimes uses a more complicated way to solve the problem), so you can add 0%-20%. Solving it yourself is imho not a good idea: you know what the solution looks like and what way the problem has to be solved and you will not find your own mistakes. Commented Nov 5, 2014 at 9:02
• @TheAlmightyBob that should be an answer, not a comment! Commented Nov 5, 2014 at 10:23
• The TA should be as fast as one of the best students so you can add 20%-50% of the time needed to the exam length — In my experience, 100%-200% is a better addition. Commented Nov 5, 2014 at 13:03
• Are you forced to fix your grading scheme before hand? If not, you can design your exam to be "too much" (which has other benefits) with the expectation that (most) students won't do everything. Observe what is actually possible (there's always that one Hermione type) and set your grades accordingly. Commented Nov 5, 2014 at 17:15
• @Raphael If I received an exam for my first test that was physically impossible to complete, I'd drop the class the day after. Presenting insurmountable problems to gauge student performance is not nice to the students. Commented Nov 5, 2014 at 17:20

This is totally unscientific, but for my exams (mathematics) I use the following rule of thumb:

After writing the exam, I sit down with a stopwatch and work the exam from start to finish. Of course, I know how to solve the problems (since I wrote them) but I go carefully through all the steps and write what I would consider a thorough and exemplary solution. I note the time I spent on each problem.

Then I take the total time and multiply it by 3 (or sometimes 4). If this exceeds the allotted time for the exam, I remove or simplify some questions. (This is where it helps that I wrote down the time I spent on each question, so I can remove a question and recompute the time without actually retaking the whole exam.)

As a side benefit, this also helps ensure that I haven't made any mistakes in creating the exam, and that all the problems have the solutions I intended. It also gives me an answer key.

• I use a factor of 5. So a one-hour exam should take 12 minutes to write. Commented Nov 5, 2014 at 18:14
• From talking my professors in undergrad, this is very similar to what they did. They always said they could finish their own 50 min exam in 15 min. Commented Nov 6, 2014 at 1:29
• I also use factor 3-4 for statistics.
– Pere
Commented Nov 27, 2016 at 2:40

in a scenario like this, are there any methods or general rules for determining how long you can make the exam, given the time allotted?

The way how I always do it is to give the exam to my student assistants (TAs, master students, undergraduate researchers), and see how long it takes them. The closer the students are to your average well-prepared course participant, the better. And, obviously, you want to add a bit of leeway to allow for the fact that your course participants, unlike your exam testers, are going to be nervous and in a test situation, and that you don't want time to matter too much.

Edit: Bob beat me to it in a comment.

In my experience, the ratio between the time needed to solve a problem by an experienced teacher and the "average student" can vary a lot, depending on the subject, the kind of problems and even between problems of the same kind. At one end, there are problems whose solutions are pretty straightforward but which require a lot of tedious calculations, for which no shortcut exists: in this case the solution time is almost the same for the professor and the students. On the other end, there are problems which require to find a "smart" solution, where few calculations are involved: in this case, an experienced professor can solve a problem in much less time (ratios of about 4 between the solution times are not uncommon).

So, even if you can give exam problems to TAs for testing, try to judge carefully what kind of problems you have prepared, this might allow you to better trim the exam duration.

I typically consider a ratio of around 3 between the exam time and my solution time (Electronic measurements).

• As the teacher, when taking the test you should be able to abstain from using shortcuts which you did not teach and as such those should not affect the time required. TA's/others may however run into them and use the shortcuts. Commented Nov 5, 2014 at 21:31
• @user2813274: I haven't written I didn't teach the shortcut. But students may fail to recognise the similarity between the example described during the lessons and the exam problem. And anyway, I expect students to be able to find shortcuts on the basis of what they've studied in all the courses they've followed, especially if they are graduate students. Commented Nov 5, 2014 at 21:43
• If you taught the shortcut (and expect the students to use it), then there is nothing wrong with allocating time and expecting students to have to use it in order to finish on time. I would not however expect them to use shortcuts from other courses, which they may or may not have taken (unless it's a prerequisite, but even then I wouldn't test on it unless it was reviewed in class first). Commented Nov 5, 2014 at 22:08
• The important thing is that the students should be aware of the expectations of their professors. So, I clearly warn them of two things: i) at the exams they will find at least a new problem, that is, a problem for which no previous example has been discussed (as exercise in class, homework or from previous exams); ii) I expect them to be able to use basic facts from a number of other subjects which are mandatory for every student, so that they not need to be explicitly stated as prerequisites. And the exam is open books. If they don't understand these expectations, too bad, they will fail. Commented Nov 6, 2014 at 1:31
• I am not sure how I feel about "new problems", so I asked a question about them - but please edit/comment if you don't mind as to what specific problems you ask. I remember some professors who did such things, but I hated them for it even when I did solve the problem. I also think that these problems will make judging the correct amount of time much more difficult that without them. Commented Nov 6, 2014 at 3:48

Here's what I do, even in courses I've taught often. It doesn't answer the question you asked, but it may serve your purpose.

I always try to make up an exam that can be done in the time alloted, but I almost never succeed - I get carried away making the questions interesting, in hopes that students will actually learn from the exam as well as demonstrate what they know. I announce my failing in advance, so students won't be surprised. I make sure to tell them that since I know there are some A students in the class, I am morally bound to curve the exam so that the top grades are A.

I tell the students that after they turn in their (timed) exam they should take the questions home and come to the next class with a paper with the solutions they wish they'd had enough time to write. I tell them that extra effort won't necessarily replace their timed work, but can improve their grade.

Since I almost always give open book open notes exams, the fact that they can look things up at home isn't a real bonus. I'm aware of the fact that they can get extra help at home (i.e. cheat) but I'm always uncomfortable designing limitations to catch cheaters that deny the majority of honest students a chance to learn more.

• Sounds very familiar, except that I always refused to assign letter grades to individual exams. I could generally say that anyone who scored at least 80% was doing A work, and anyone who scored at least 50% was doing at least C work. And I do remember a small class or two in which there really was no one who deserved an A at the end of the course. Commented Nov 6, 2014 at 12:40

If the person setting the exam has no idea how the questions are going to play in practice, the students are presumably in exactly the same situation. That may add to nervousness issues, and make it hard for them to prepare for the test.

How about giving a practice exam, which may be shorter than the real thing but use similar questions, during a class period a couple of weeks before the actual exam? If you do the questions yourself, or have a TA etc. do them as already suggested, you can use the practice test to calibrate the ratio between the time for the actual students and the TA's time.

The students will also benefit by seeing what sort of questions you pose, with an opportunity to discuss them with you, with the TA, and among themselves. That will help them prepare for the actual test.

• I don't have a free period to give a practice exam in. The students have seen the type of questions I will pose because they were given for homework, but I haven't seen the students do those types of questions. Commented Nov 5, 2014 at 18:01
• @ff524, find a free period that MOST of your student can make and have the practice exam being optional, with other students being able to do it at home if the can't make the time you set.
– Ian
Commented Jan 25, 2016 at 15:08
• I doubt students would make the practice exam at the same speed of the actual exam, unless they think the practice exam is going to be graded.
– Pere
Commented Nov 27, 2016 at 2:43

I like Nate's suggestion to multiply by 4 if your exam is all essay questions. If you're concerned about students not finishing, you could use multiple choice and short answer questions.

Multiple choice and short answer questions force you to ask focused questions that can be answered quickly. When I was in undergrad, I always liked test that were multiple choice and short answer because I knew that each multiple choice question would take 1-2 minutes, each short answer 2-3 and the essay question would usually take 7-10.

You could use those rules of thumb to build out a test that you are sure students will be able to finish.

You might find This multiple choice test primer helpful.

• That's a good link, although I'm not sure how much this answers the original questions. Commented Nov 5, 2014 at 18:17
• The other post beat me to suggesting take it yourself and multiply the time by 4, and giving it to the TA. Commented Nov 5, 2014 at 18:26
• What you say is not strictly true. In general, the format of a question does not necessarily tell you anything about the time that will be needed to answer it. A multiple choice question might require you to solve an arbitrarily complex problem to get the answer. I can write a multiple choice question that will literally take trillions of years to answer correctly :-) Commented Nov 6, 2014 at 14:06
• Quite true, you can make a bad exam using multiple choice. In my experience as a student and grader, multiple choice exams tend NOT to take 4 times longer than the prof thought, and not end up with the highest grade being 32/100, which I've seen happen quite often with essay style exams. Commented Nov 6, 2014 at 14:59

Exam Time Calibration

• 1/8 time for professor to solve a freshman level exam
• 1/7 time for professor to solve a sophomore level exam
• 1/6 time for professor to solve a junior level exam
• any above could limit to a factor of 5 by handwriting speed, treat as "1/5" for all undergraduate
• 1/5 time for professor to solve a senior level exam
• 1/4 time for professor to solve a elementary graduate (master) level exam
• 1/3 time for professor to solve a intermediate graduate (specialized master) level exam
• 1/2 time for professor to solve an advance graduate (doctor) level exam

The rule of thumb is to time yourself writing an answer key with all required steps. Multiply by an appropriate factor as necessary. The factor is the inverse of the expected time to solve the problem yourself.

I remember taking a final exam for a Master level class, and I finished in one hour, one classmate finished in two hours, third person took four hours, while the rest of my classmates took five hours. The lower third of the class did not finish the exam after 5 hours. The exam was scheduled for three hours.

I remember noting down the time in 30 seconds increment I took for each problem on a homework assignment, so my professor wrote his time writing the answer key right next to each of my times. I was faster overall and on most problems (youth thinks faster), but slower on some problems (wisdom thinks smarter).